Grade 10 Maths · Functions · Paper 1

Graph Interpretation Grade 10

Real Graph Interpretation past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 9 past paper questions
skills: 3 skills
videos: 3 videos

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Question 5.2 · June 2025 · Paper 1 · Provincial · 6 marks

Given:

f (x) = - x + 1

and

g (x) = \frac{- 2}{x} + 2

, which are not drawn to scale. R and S are points of intersection of the graphs.

DBQ is a line perpendicular to the x-axis with D and B on

g

and

f

respectively. The coordinates of Q are

(- 1; 0)

5.2 Determine the coordinates of R and S.(6)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Graph Interpretation skills

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More Graph Interpretation Grade 10 questions and answers

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4. Question 4.1.3 · June 2025 · Paper 1 · Provincial · 2 marks
4.1 Given: $f (x) = - x^{2} + 4$
4.1.3 Determine the value(s) of $x$ for which $f (x) > 0$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Interval between the $x$ -intercepts $- 2$ and $2$ : the graph is above the $x$ -axis between them
  1 mark · Solve an inequality from a graph
2. ✓
  Notation $- 2 < x < 2$ OR $x \in (- 2; 2)$ (strict signs or round brackets, because $f (x) > 0$ , not $\geq 0$ )
  1 mark · Solve an inequality from a graph
5. Question 6.1.2 · September 2024 · Provincial · 4 marks
6.1 Given: $f (x) = 2 sin x + 1$ and $g (x) = tan x$ , where $x \in [0^{\circ}; 27 0^{\circ}]$
6.1.2 On the same set of axes provided on the DIAGRAM SHEET, sketch the graphs of f and g. Clearly indicate all intercepts with the axes, as well as turning points and end points of the graphs.(4)
Show the memo (4 ticks)Memo
1. ✓
  Shape of fSine curve for $f (x) = 2 sin x + 1$ from $(0^{\circ}; 1)$ to $(27 0^{\circ}; - 1)$
  1 mark · Sketch a trig graph
2. ✓
  Shape of gTan curve for $g (x) = tan x$ through $(0^{\circ}; 0)$ and $(18 0^{\circ}; 0)$
  1 mark · Sketch a trig graph
3. ✓
  Asymptotes of g $x = 9 0^{\circ}$ and $x = 27 0^{\circ}$
  1 mark · Sketch a trig graph
4. ✓
  Turning point of f $(9 0^{\circ}; 3)$
  1 mark · Sketch a trig graph
6. Question 5.5 · November 2024 · Paper 2 · Provincial · 1 mark
In the diagram below, the graphs of $f (x) = cos x + a$ and $g (x) = b sin x$ are drawn for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
5.5 Determine the number of solutions to $f (x) = g (x)$ for $- 18 0^{\circ} < x < 18 0^{\circ}$ .(1)
Show the memo (1 tick)Memo
1. ✓
  Count intersections $1$ solution
  1 mark · Plot and read points

Graph Interpretation Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Vertical Distance Grade 11 FunctionsKevinmathscience

Parabola + Straight Line| Grade 11 FunctionsKevinmathscience

f(x) bigger than 0 | Grade 11 FunctionsKevinmathscience

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